# Velocity-time graphs

If an object moves along a straight line, its motion can be represented by a velocity-time graph. The gradient of the line is equal to the acceleration of the object.

The table shows what each section of the graph represents:

Apostiveincreasingpostive
Bzeroconstantzero
Cnegativedecreasingnegative
Dzerostationary (at rest)zero

### Example

Describe the motion of the vehicle in the graph at the three stages of its journey.

Between 0 s and 4 s the vehicle is accelerating.

This means that:

Between 4 s and 7 s the vehicle has a constant velocity of 8 m/s.

Between 7 s and 10 s, the vehicle is decelerating so:

## Calculating displacement - Higher

The of an object can be calculated from the area under a velocity-time graph.

The area under the graph can be calculated by:

• using geometry (if the lines are straight)
• counting the squares beneath the line (particularly if the lines are curved)

### Example

Calculate the total displacement of the object whose motion is represented by the velocity-time graph below.

The displacement can be found by calculating the total area of the shaded sections below the line.

Find the area of the triangle:

Find the area of the rectangle:

base × height

(10 - 4) × 8 = 48 m2

Add the areas together to find the total displacement:

(16 + 48) = 64 m

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